fdesign.highpass

Highpass filter specification object

Syntax

D = fdesign.highpass D = fdesign.highpass(SPEC) D = fdesign.highpass(SPEC,specvalue1,specvalue2,...) D = fdesign.highpass(specvalue1,specvalue2,specvalue3, specvalue4) D = fdesign.highpass(...,Fs) D = fdesign.highpass(...,MAGUNITS)

Description

D = fdesign.highpass constructs a highpass filter specification object D, applying default values for the specification, 'Fst,Fp,Ast,Ap'.

D = fdesign.highpass(SPEC) constructs object D and sets the Specification property to SPEC. Entries in the SPEC represent various filter response features, such as the filter order, that govern the filter design. Valid entries for SPEC are shown below. These entries are not case sensitive.

Note

Specification entries marked with an asterisk require the DSP System Toolbox™ software.

'Fst,Fp,Ast,Ap' (default spec)
'N,F3db'
'N,F3db,Ap' *
'N,F3db,Ast' *
'N,F3db,Ast,Ap' *
'N,F3db,Fp *
'N,Fc'
'N,Fc,Ast,Ap'
'N,Fp,Ap'
'N,Fp,Ast,Ap'
'N,Fst,Ast'
'N,Fst,Ast,Ap'
'N,Fst,F3db' *
'N,Fst,Fp'
'N,Fst,Fp,Ap' *
'N,Fst,Fp,Ast' *
'Nb,Na,Fst,Fp' *

The filter specifications are defined as follows:

Ap — amount of ripple allowed in the pass band in decibels (the default units). Also called Apass.
Ast — attenuation in the stop band in decibels (the default units). Also called Astop.
F3db — cutoff frequency for the point 3 dB point below the passband value. Specified in normalized frequency units.
Fc — cutoff frequency for the point 6 dB point below the passband value. Specified in normalized frequency units.
Fp — frequency at the start of the pass band. Specified in normalized frequency units. Also called Fpass.
Fst — frequency at the end of the stop band. Specified in normalized frequency units. Also called Fstop.
N — filter order.
Na and Nb are the order of the denominator and numerator.

Graphically, the filter specifications look similar to those shown in the following figure.

Regions between specification values like Fst and Fp are transition regions where the filter response is not explicitly defined.

The filter design methods that apply to a highpass filter specification object change depending on the Specification. Use designmethods to determine which design method applies to an object and its specification.

Use designopts to determine which design options are valid for a given design method. For detailed information on design options for a given design method, METHOD, enter help(D,METHOD) at the MATLAB^® command line.

D = fdesign.highpass(SPEC,specvalue1,specvalue2,...) constructs an object d and sets its specification values at construction time.

D = fdesign.highpass(specvalue1,specvalue2,specvalue3, specvalue4) constructs an object D with the default Specification property and the values you enter for specvalue1,specvalue2,....

D = fdesign.highpass(...,Fs) provides the sampling frequency for the filter specification object. Fs is in Hz and must be specified as a scalar trailing the other numerical values provided. If you specify a sampling frequency, all other frequency specifications are in Hz.

D = fdesign.highpass(...,MAGUNITS) specifies the units for any magnitude specification you provide in the input arguments. MAGUNITS can be one of

'linear' — specify the magnitude in linear units
'dB' — specify the magnitude in dB (decibels)
'squared' — specify the magnitude in power units

When you omit the MAGUNITS argument, fdesign assumes that all magnitudes are in decibels. Note that fdesign stores all magnitude specifications in decibels (converting to decibels when necessary) regardless of how you specify the magnitudes.

Examples

collapse all

Design Butterworth Filter

Open Live Script

Design a Butterworth filter with lowpass and highpass frequency responses. The filter design procedure is:

Specify the filter design specifications using a fdesign function.
Pick a design method provided by the designmethods function.
To determine the available design options to choose from, use the designoptions function.
Design the filter using the design function.

Lowpass Filter

Construct a default lowpass filter design specification object using fdesign.lowpass.

designSpecs = fdesign.lowpass

designSpecs = 
  lowpass with properties:

               Response: 'Lowpass'
          Specification: 'Fp,Fst,Ap,Ast'
            Description: {4x1 cell}
    NormalizedFrequency: 1
                  Fpass: 0.4500
                  Fstop: 0.5500
                  Apass: 1
                  Astop: 60

Determine the available design methods using the designmethods function. To design a Butterworth filter, pick butter.

designmethods(designSpecs,SystemObject=true)

Design Methods that support System objects for class fdesign.lowpass (Fp,Fst,Ap,Ast):


butter
cheby1
cheby2
ellip
equiripple
ifir
kaiserwin
multistage

While designing the filter, you can specify additional design options. View a list of the options using the designoptions function. This function also shows the default design options the filter uses.

designoptions(designSpecs,'butter',SystemObject=true)

ans = struct with fields:
           FilterStructure: {'df1sos'  'df2sos'  'df1tsos'  'df2tsos'  'cascadeallpass'  'cascadewdfallpass'}
              SOSScaleNorm: 'ustring'
              SOSScaleOpts: 'fdopts.sosscaling'
              MatchExactly: {'passband'  'stopband'}
    DefaultFilterStructure: 'df2sos'
       DefaultMatchExactly: 'stopband'
       DefaultSOSScaleNorm: ''
       DefaultSOSScaleOpts: [1x1 fdopts.sosscaling]

Use the design function to design the filter. Pass 'butter' and the specifications given by variable designSpecs, as input arguments. Specify the 'matchexactly' design option to 'passband'.

lpFilter = design(designSpecs,'butter',matchexactly='passband',SystemObject=true)

lpFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [13x3 double]
          Denominator: [13x3 double]
       HasScaleValues: true
          ScaleValues: [0.4095 0.3669 0.3330 0.3059 0.2841 0.2666 0.2525 0.2414 0.2328 0.2263 0.2219 0.2193 0.4674 1]

  Use get to show all properties

Visualize the frequency response of the designed filter.

filterAnalyzer(lpFilter)

Highpass Filter

Construct a highpass filter design specification object using fdesign.highpass. Specify the order to be 7 and the 3 dB frequency to be $0.6 π$ radians/sample.

designSpecs = fdesign.highpass('N,F3dB',7,.6)

designSpecs = 
  highpass with properties:

          Specification: 'N,F3dB'
               Response: 'Highpass'
            Description: {2x1 cell}
    NormalizedFrequency: 1
            FilterOrder: 7
                   F3dB: 0.6000

Determine the available design methods. To design a Butterworth filter, pick butter.

designmethods(designSpecs,SystemObject=true)

Design Methods that support System objects for class fdesign.highpass (N,F3dB):


butter
maxflat

designoptions(designSpecs,'butter',SystemObject=true)

ans = struct with fields:
           FilterStructure: {'df1sos'  'df2sos'  'df1tsos'  'df2tsos'  'cascadeallpass'  'cascadewdfallpass'}
              SOSScaleNorm: 'ustring'
              SOSScaleOpts: 'fdopts.sosscaling'
    DefaultFilterStructure: 'df2sos'
       DefaultSOSScaleNorm: ''
       DefaultSOSScaleOpts: [1x1 fdopts.sosscaling]

To design the Butterworth filter, use the design function and specify 'butter' as an input. Set 'FilterStructure' to 'cascadeallpass'.

hpFilter = design(designSpecs,'butter',FilterStructure='cascadeallpass',SystemObject=true)

hpFilter = 
  dsp.CoupledAllpassFilter with properties:

               Structure: 'Minimum multiplier'
         PureDelayBranch: 0
    AllpassCoefficients1: {2x1 cell}
    AllpassCoefficients2: {2x1 cell}
                   Gain1: '-1'
                   Gain2: '1'

Visualize the highpass frequency response.

filterAnalyzer(hpFilter)

Highpass Filtering of Sinusoids

Open Live Script

Highpass filter a discrete-time signal consisting of two sine waves.

Create a highpass filter specification object. Specify the passband frequency to be 0.25π rad/sample and the stopband frequency to be 0.15π rad/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB.

d = fdesign.highpass('Fst,Fp,Ast,Ap',0.15,0.25,60,1);

Query the valid design methods for your filter specification object.

designmethods(d)

Design Methods for class fdesign.highpass (Fst,Fp,Ast,Ap):


butter
cheby1
cheby2
ellip
equiripple
ifir
kaiserwin

Create an FIR equiripple filter and view the filter magnitude response.

Hd = design(d,'equiripple');
freqz(Hd)

$Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.$

Create a signal consisting of the sum of two discrete-time sinusoids with frequencies of π/8 and π/4 rad/sample and amplitudes of 1 and 0.25 respectively. Filter the discrete-time signal with the FIR equiripple filter object.

n = 0:159;
x = cos(pi/8*n)+0.25*sin(pi/4*n);
y = filter(Hd,x);

Plot the original and filtered signals in the frequency domain.

freq = 0:(2*pi)/160:pi;
xdft = fft(x);
ydft = fft(y);

plot(freq/pi,abs(xdft(1:length(x)/2+1)))
hold on
plot(freq/pi,abs(ydft(1:length(y)/2+1)),'r','linewidth',2)
hold off
legend('Original Signal','Lowpass Signal','Location','NorthEast')
ylabel('Magnitude')
xlabel('Normalized Frequency (\times\pi rad/sample)')

Figure contains an axes object. The axes object with xlabel Normalized Frequency ( times pi blank rad/sample), ylabel Magnitude contains 2 objects of type line. These objects represent Original Signal, Lowpass Signal.

Window Method Highpass Design

Open Live Script

Create a filter of order 10 with a 6-dB frequency of 9.6 kHz and a sample rate of 48 kHz. Look at the available design methods.

d=fdesign.highpass('N,Fc',10,9600,48000);
designmethods(d)

Design Methods for class fdesign.highpass (N,Fc):


window

The only available method is the FIR window method. Design the filter and display its magnitude response.

Hd = design(d);
freqz(Hd)

Stopband Constraints

Open Live Script

You can specify the shape of the stopband and the rate at which the stopband decays.

Create two FIR equiripple filters with different linear stopband slopes. Specify the passband frequency to be 0.3π rad/sample and the stopband frequency to be 0.35π rad/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB. Design one filter with a 20 dB/(rad/sample) stopband slope and another filter with a slope of 40 dB/(rad/sample).

D = fdesign.highpass('Fst,Fp,Ast,Ap',0.3,0.35,60,1);
Hd1 = design(D,'equiripple',StopBandShape='linear',...
    StopBandDecay=20,SystemObject=true);
Hd2 = design(D,'equiripple',StopBandShape='linear',...
    StopBandDecay=40,SystemObject=true);

Visualize the magnitude responses of the filters.

hvft = filterAnalyzer(Hd1,Hd2);
setLegendStrings(hvft,["20 dB/(rad/sample)","40 dB/(rad/sample)"])

Version History

Introduced in R2009a

fdesign.highpass

Syntax

Description

Examples

Design Butterworth Filter

Highpass Filtering of Sinusoids

Window Method Highpass Design

Stopband Constraints

Version History

See Also